The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the issuer is liable for the net loss. In this article, the mathematical foundation for ...The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the issuer is liable for the net loss. In this article, the mathematical foundation for pricing the European passport option is established. The pricing equation which is a fully nonlinear equation is derived using the dynamic programming principle. The comparison principle, uniqueness and convexity preserving of the viscosity solutions of related H J13 equation are proved. A relationship between the passport and lookback options is discussed.展开更多
In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options...In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options. From the viscosity solution of a PDE, a unique viscosity solution was obtained for the semilinear Black-Scholes PDE.展开更多
In this study,we estimated the weekly Gravity Recovery and Climate Experiment(GRACE)spherical harmonic(SH)solutions and regional mascon solutions using GRACE-based Geopotential Difference(GPD)data and investigated the...In this study,we estimated the weekly Gravity Recovery and Climate Experiment(GRACE)spherical harmonic(SH)solutions and regional mascon solutions using GRACE-based Geopotential Difference(GPD)data and investigated their abilities in retrieving terrestrial water storage(TWS)changes over the Amazon River Basin(ARB)from January 2003 to February 2013.The performance of the weekly GPD-SH and GPDmascon solutions was evaluated by comparing them with the weekly GFZ-SH solutions,Global Land Data Assimilation Systems(GLDAS)-NOAH hydrological model outputs,and monthly GFZ-SH,GPD-SH,and CSRmascon solutions in the spatio-temporal and spectral domains.The results demonstrate that the weekly GPD-SH and GPD-mascon present good consistency with the weekly GFZ-SH solutions and GLDAS-NOAH estimates in the spatio-temporal domains,but GPD-mascon presents stronger signal amplitudes and more spatial details.The comparison of the monthly average of weekly estimates and monthly solutions demonstrates that the weekly GPD-mascon and GFZ-SH with DDK1 filtering are close to the monthly CSRmascon and GFZ-SH solutions,respectively.However,the signal amplitudes of TWS changes from GPD-SH and GFZ-SH with 650 km Gaussian filtering are smaller than the monthly solutions,and the corresponding Root Mean Square Errors between the TWS change time series from the monthly average of weekly solutions and monthly estimates are 18.12 mm(GPD-mascon),18.81 mm(GFZ-SH-DDK1),24.93 mm(GPDSH-G650km),and 33.07 mm(GFZ-SH-G650km),respectively.Additionally,the TWS change time series derived from weekly solutions present more high-frequency time-varying information than monthly solutions.Furthermore,the 300 km Gaussian filtering can improve the signal amplitudes of TWS changes from the weekly GPD-SH solutions more than those with 650 km Gaussian filtering,but the corresponding noise level is higher.The weekly GPD-SH and GPD-mascon solutions can extend the application scopes of GRACE and provide good complements to the current GRACE monthly solutions.展开更多
We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing therma...We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model.We derive a three-dimensional Fast Fourier Transform(“FFT”)lower bound approximation to value the inherent real optionality and for robustness check,we compare the semi-analytical pricing accuracy with the Monte Carlo simulation.Model parameters are estimated from the historical monthly data,and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross(“CIR”)model.展开更多
Transdermal medications are an useful yet underutilized tool in the field of psychiatry.Despite numerous advantages of using this route of medication delivery,transdermal medications remain less popular compared to ot...Transdermal medications are an useful yet underutilized tool in the field of psychiatry.Despite numerous advantages of using this route of medication delivery,transdermal medications remain less popular compared to other routes of medication administration such as oral and intramuscular routes in the management of various psychiatric conditions.In this editorial,we examine the advantages of transdermal medications with a brief overview of transdermal being used in psychiatry and other medical specialties.We discuss the factors that play a role in their limited usage in psychiatry.We highlight certain patient categories who can specifically benefit from them and discuss potential solutions that can broaden the perspective of treating clinicians making this an intriguing avenue in the field of psychiatry.展开更多
The Bermudan option pricing problem with variable transaction costs is considered for a risky asset whose price process is derived under the information-based model. The price is formulated as the value function of an...The Bermudan option pricing problem with variable transaction costs is considered for a risky asset whose price process is derived under the information-based model. The price is formulated as the value function of an optimal stopping problem, which is the value function of a stochastic control problem given by a non-linear second order partial differential equation. The theory of viscosity solutions is applied to solve the stochastic control problem such that the value function is also the solution of the corresponding Bellman equation. Under some regularity assumptions, the existence and uniqueness of the solution of the pricing equation are derived by the application of the Perron method and Banach Fixed Point theorem.展开更多
基金supported in partby National Science Foundation of China (10371088,10671144)National Basic Research Program of China(2007CB814903)+3 种基金Development Funds of Shanghai Higher Education (05D210)the Special Funds for Major Specialties of Shanghai Education Committee (T0401)Supported by Special Fund for the Excellent Young Teachers of Shanghai Higher Learning Institutions (ssd08029)the Research Program of Shanghai Normal University (SK200812)
文摘The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the issuer is liable for the net loss. In this article, the mathematical foundation for pricing the European passport option is established. The pricing equation which is a fully nonlinear equation is derived using the dynamic programming principle. The comparison principle, uniqueness and convexity preserving of the viscosity solutions of related H J13 equation are proved. A relationship between the passport and lookback options is discussed.
基金Project supported by the National Natural Science Foundation of China (Grant No.10271072)
文摘In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options. From the viscosity solution of a PDE, a unique viscosity solution was obtained for the semilinear Black-Scholes PDE.
基金funded by the National Natural Science Foundation of China(Nos.41974015,42374002)the Project Supported by the Special Fund of Hubei Luojia Laboratory(No.220100004)。
文摘In this study,we estimated the weekly Gravity Recovery and Climate Experiment(GRACE)spherical harmonic(SH)solutions and regional mascon solutions using GRACE-based Geopotential Difference(GPD)data and investigated their abilities in retrieving terrestrial water storage(TWS)changes over the Amazon River Basin(ARB)from January 2003 to February 2013.The performance of the weekly GPD-SH and GPDmascon solutions was evaluated by comparing them with the weekly GFZ-SH solutions,Global Land Data Assimilation Systems(GLDAS)-NOAH hydrological model outputs,and monthly GFZ-SH,GPD-SH,and CSRmascon solutions in the spatio-temporal and spectral domains.The results demonstrate that the weekly GPD-SH and GPD-mascon present good consistency with the weekly GFZ-SH solutions and GLDAS-NOAH estimates in the spatio-temporal domains,but GPD-mascon presents stronger signal amplitudes and more spatial details.The comparison of the monthly average of weekly estimates and monthly solutions demonstrates that the weekly GPD-mascon and GFZ-SH with DDK1 filtering are close to the monthly CSRmascon and GFZ-SH solutions,respectively.However,the signal amplitudes of TWS changes from GPD-SH and GFZ-SH with 650 km Gaussian filtering are smaller than the monthly solutions,and the corresponding Root Mean Square Errors between the TWS change time series from the monthly average of weekly solutions and monthly estimates are 18.12 mm(GPD-mascon),18.81 mm(GFZ-SH-DDK1),24.93 mm(GPDSH-G650km),and 33.07 mm(GFZ-SH-G650km),respectively.Additionally,the TWS change time series derived from weekly solutions present more high-frequency time-varying information than monthly solutions.Furthermore,the 300 km Gaussian filtering can improve the signal amplitudes of TWS changes from the weekly GPD-SH solutions more than those with 650 km Gaussian filtering,but the corresponding noise level is higher.The weekly GPD-SH and GPD-mascon solutions can extend the application scopes of GRACE and provide good complements to the current GRACE monthly solutions.
文摘We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model.We derive a three-dimensional Fast Fourier Transform(“FFT”)lower bound approximation to value the inherent real optionality and for robustness check,we compare the semi-analytical pricing accuracy with the Monte Carlo simulation.Model parameters are estimated from the historical monthly data,and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross(“CIR”)model.
文摘Transdermal medications are an useful yet underutilized tool in the field of psychiatry.Despite numerous advantages of using this route of medication delivery,transdermal medications remain less popular compared to other routes of medication administration such as oral and intramuscular routes in the management of various psychiatric conditions.In this editorial,we examine the advantages of transdermal medications with a brief overview of transdermal being used in psychiatry and other medical specialties.We discuss the factors that play a role in their limited usage in psychiatry.We highlight certain patient categories who can specifically benefit from them and discuss potential solutions that can broaden the perspective of treating clinicians making this an intriguing avenue in the field of psychiatry.
文摘The Bermudan option pricing problem with variable transaction costs is considered for a risky asset whose price process is derived under the information-based model. The price is formulated as the value function of an optimal stopping problem, which is the value function of a stochastic control problem given by a non-linear second order partial differential equation. The theory of viscosity solutions is applied to solve the stochastic control problem such that the value function is also the solution of the corresponding Bellman equation. Under some regularity assumptions, the existence and uniqueness of the solution of the pricing equation are derived by the application of the Perron method and Banach Fixed Point theorem.
